In this paper, a novel quadratic assignment-based mathematical model is developed for concurrent design of robust inter and intra-cell layouts in dynamic stochastic environments of manufacturing systems. In the proposed model, in addition to considering time value of money, the product demands are presumed to be dependent normally distributed random variables with known expectation, variance, and covariance that change from period to period at random. This model is verified and validated by solving a number of different-sized test problems and a real world problemas well as doing sensitivity analysisby using the analysis of variance (ANOVA) technique.The validation process will be ended by investigating the effect of considering dependent product demands and time value of money (interest rate) on the total cost. Dynamic programming andsimulated annealing algorithms programmed in Matlab are used to solve the problems.Some conclusions can be summarised as follows: (i) the simulated annealing algorithm has a performance as good as the dynamic programming algorithm from solution quality point of view; (ii) the simulated annealingis a robust algorithm; (iii) different values of the input parameters lead to design of different facility layouts; (iv) total cost of inter and intra-cell layouts is affected by the interest rate and the percentile level; and (v) the proposed model can be used in both of the stochastic and deterministic environments.

Irappa-Basappa, H., & Madhusudanan-Pillai, V. (2008). Development of a heuristic for layout formation and design of robust layout under dynamic demand. Proceedings of the International Conference on Digital Factory, ICDF 2008, August 11-13, 1398 -1405.

Ji, P., Yongzhong, W., & Haozhao, L. (2006). A Solution Method for the Quadratic Assignment Problem (QAP). The Sixth International Symposium on Operations Research and Its Applications (ISORA’06) Xinjiang, China, August 8–12, 106–117.